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In the last video we defined
internal energy as literally

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all the energy that's
in a system.

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That's kind of the most
inclusive version,

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at least in my head.

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So that's my system, it's
some type of container.

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And I have a bunch of
particles in here.

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It's literally the sum of
the kinetic energies

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of all these particles.

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If they had potential
energies, we'd

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throw that in there.

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If they have electrical
potential, we'd

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throw that in there.

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If they have bonds with each
other, the energies in that

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bond, we would throw
it in there.

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It's everything.

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It's all inclusive.

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And, I told you in the last
video it's unintuitive that U

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stands for internal energy.

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But I kind of think that, you
know, U, it contains the

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universe of energy.

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You know, that's just for
me to memorize it.

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Don't think too deeply into
what I just said.

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But this is internal energy.

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If you show me a system, it
has some internal energy.

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It's a function of its state.

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I don't care how it got to that
state, but if you told me

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a system at a certain state,
maybe with a certain pressure,

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or a certain volume, or at a
certain temperature-- although

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if you give me pressure and
volume that should be enough--

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I can tell you what its
internal energy is.

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Especially if you tell me the
type of molecule I have, and

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things like that.

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Now we also said in the last
video that because internal

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energy is all the energy in
the system, it can't be

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randomly created or destroyed.

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It can just be transformed
from one form to another.

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So if I have a change in
internal energy, it can only

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be due to-- well, it can be
due to more than what I'm

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describing.

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But in our simple world where
all of the energy in a

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system-- and maybe we're dealing
with gases, because

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that's normally what you deal
with in a first-year chemistry

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course-- it's going to be the
heat that could be added to

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the system, plus the work
done on the system.

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And like I said in the last
video, sometimes they'll say,

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instead of plus the work done
on the system, sometimes

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they'll say, minus the work
that the system does.

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Either way.

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And here I just want to make
another side discussion here,

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because I decided to write
it without the

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little deltas here.

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And the reason why I did that
is if you were to write this

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equation, which you will see,
you'll see it in textbooks,

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teachers will do it-- nothing
inherently criminal about

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that-- but I just do that
because it clears in my mind

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what heat and what work are
relative to internal energy.

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If I were to write delta U is
equal to heat delta Q plus

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delta W to me this implies that
at some point I had some

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amount of heat in my system,
and then I have a different

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amount of heat in my system,
and I took the difference

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between the two and I got
a change in heat.

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So this implies that heat is
somehow an inherent macrostate

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of the system, and that's
not the case.

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I can tell you what the
internal energy

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of this system is.

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I can tell you its pressure.

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I can tell you its volume.

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I can tell you its
temperature.

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These are all macrostates
of the system.

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I don't know how it got to this
situation, but I can tell

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you about it.

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I cannot tell you what the
heat is of this system.

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And that might be a little
unintuitive, because if I ask

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you, hey I have a cup of coffee,
what's the heat of it?

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You might say, oh, it's, you
know, you might give me the

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temperature.

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Because in our everyday language
we use things like

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heat and temperature
interchangeably.

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But in thermodynamics, heat
is a transfer of energy.

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A way to think about it
is, if internal energy

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is your bank account.

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So you could say change
in bank account.

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And it really is like
the energy bank

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account of a system.

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If you have a change in a bank
account, you had some deposits

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or withdrawals.

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And heat and work are really
just deposits or withdrawals

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into our energy bank account.

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Heat is one kind.

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Maybe heat is like
a wire transfer.

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So you could say it's wire
transfers to your account.

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Transfers to your account
plus check deposits.

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Now it makes a lot of sense to
say, you could say, what is my

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value of my bank account?

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Or you could say what is my
change in my bank account?

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You take two snapshots of
your bank account at

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two different times.

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But would it make sense to say--
you know, I could say I

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wire transferred $10, right?

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So I could say, this statement
would be plus $10.

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And I could say that I
wrote $20 in checks,

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minus $20 in checks.

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In which case, my change
in my bank account

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would be minus $10.

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Now would it make sense
for me to say

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change in wire transfer?

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That implies that when I started
off maybe my bank

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account had $100 in it
and now it has $90.

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When my bank account had $100
in it, did it have any wire

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transfer amount?

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No, wire transfer was how money
was deposited or taken

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away from my account.

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Likewise, it didn't have a
checking deposit account, so I

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can't really-- it just seems
weird to me to say change in

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wire transfer is $10, or change
in check deposits is

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$20 or minus $20.

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Would you say, I made a
$10 wire transfer and

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I paid $20 in checks.

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So I had a net change in
my bank account of $10.

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Likewise, I say how much work
was done to me or I did, which

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is essentially a deposit or
withdrawal of energy.

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Or I could say much heat was
given to me or how much heat

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was released, which is another
way of depositing or

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withdrawing energy from my
energy bank account.

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So that's why I like
to stick to this.

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And I like to stay
away from this.

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And just like I said, you can't
say how much heat is in

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the system.

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So someone will say, oh, how
much heat is in this?

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You cannot say that.

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There's no heat state variable
for that system.

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You have internal energy.

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The closest thing to heat,
we'll talk about it in a

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future video, is enthalpy.

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Enthalpy is essentially a way of
measuring how much heat is

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in a system, but we won't talk
about that just now.

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And you can't say how much
work is in a system.

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You can't say, oh I have x
amount of work in a system.

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The system can do work or have
work done to it, but there's

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not a certain amount of work,
because that energy in the

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system could be all used for
work, it could all be used for

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heat, it could all be used for
a ton of different things.

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So you can't say those things.

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And that's why I don't like
treating them like state

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variables, or state functions.

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So with that said, this
is our definition.

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Let's do a couple of
simple problems,

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just to give you intuition.

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And I really want to make
you comfortable.

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My real goal is to make you
comfortable with, when to know

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to use plus or minus
on the work.

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And the best way to do it is not
to memorize a formula, but

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just to kind of think about
what's happening.

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So let's say that I have some
system here and, I don't know,

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it's a balloon.

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And let's say that I have no
change in internal energy.

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Internal energy is 0.

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And for our purposes we can kind
of view it as the kinetic

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energy of the particles
haven't changed.

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And let's say by expanding a
bit, by my balloon expanding a

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bit-- I did some work.

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I'll do this in more detail
in the next video.

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So the system does 10
joules of work.

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My question is, how much heat
was added or taken away from

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the system?

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So the way I can think about
it-- you don't even have to

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write the formula down, or you
can write it-- you could say,

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look, the internal energy, the
amount of energy in the system

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hasn't changed.

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The system did 10
joules of work.

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So that's energy going
out of the system.

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It did 10 joules.

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So 10 joules went out
in the form of work.

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If the internal energy did not
change, then essentially 10

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joules of energy had to
go into the system.

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10 joules had to go
into the system.

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If it didn't, the internal
energy would have gone down by

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the amount of work we had.

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And the only way, if is this is
the net work, the only way

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that we're talking about, that
we can add energy outside of

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work, is through heat.

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So 10 joules of heat must
have been added.

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So we can write 10 joules
of heat added to system.

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Now let's look at that from
the point of view of the

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actual formula.

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If we have delta U is equal to
heat added, plus work done to

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the system, then we would
say, OK, this was 0.

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It's equal to the heat
added to the system.

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Remember, in this way we're
saying this is the heat done,

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or the work done,
to the system.

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W is work done.

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Now, the system did work
to something else.

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It didn't have work
done to it.

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So if this is work done to the
system, and it did work, then

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this is going to
be a minus 10.

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Minus 10 joules.

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And then you solve both
sides of this.

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You add 10 to both sides and
you get 10 is equal to Q,

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which is exactly what
we got up here.

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But this can get confusing
sometimes, because you're

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like, oh, is this heat
that the system did?

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Is this heat that was added to
the system or taken away?

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The convention tends to be
that this is heat added.

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But then sometimes
it's confusing.

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Is this the work done to the
system or work done by?

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And that's why I like just
doing it this way.

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If the system does work
it loses energy.

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If the system has work done
to it, it gains energy.

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So let's do another problem.

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I mean, I could have done this
exact same thing using the

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other formula that you'll
sometimes see.

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Delta U is equal to Q minus the
work that the system does

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by the system-- Work
done by the system.

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And in this case, once
again, change in

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internal energy was 0.

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That is equal to heat
added to the system,

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minus the work done.

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So minus-- I told you at the
beginning of the problem that

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the system did 10 joules of
work-- so minus the work done.

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Minus 10 joules.

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We get the same situation
up here from

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two different formulas.

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And we got 10 is equal to Q.

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Either way, the heat added to
the system is 10 joules.

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Let's do one more.

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Let's say that, I don't know,
5 joules of heat taken away

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from system.

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And let's say that 1 joule
of work done on system.

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So maybe we're compressing the
balloon on the system.

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What is our change in
internal energy?

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Let's just figure
out our change.

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So the way I think of it is 5
joules of heat taken away from

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the system, that's going
to reduce our internal

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energy by minus 5.

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And if 1 joule work is done onto
the system, we're putting

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energy into it so that'll
be plus 1.

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So minus 5, plus 1, is
going to be minus 4.

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Or enter our change in internal

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energy is minus 4 joules.

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Now we could have done that a
little bit more formally with

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the formula, change in internal
energy is equal to

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heat added to the system, plus
work done on the system.

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So it's equal to heat
added to the system.

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We had 5 joules heat taken away,
so this is minus 5, plus

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work done on the system.

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We have 1 joule of work done
on the system, and there we

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get, once again, minus 4.

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Now, I could have written that
same formula the other way.

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I could have said change in
internal energy is equal to

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heat added to the system minus
the work that the system does.

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I want to do this both ways,
because I don't want you to

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get confused, either way you
see it on problems or in

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school, or maybe you take one
class that does it one way and

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one class that does
it the other.

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If you use it this way,
what was the heat

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added to the system?

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We had heat taken away,
so it's minus 5.

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So minus the work that the
system does, how much work

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does the system do?

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Well, the system had 1 joule
of work done to it.

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So it did itself minus
1 joules of work.

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So it's minus minus 1.

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I want to be clear, when I use
this formula, this is work

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done by system, done by.

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This is work done to.

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The system had work
done to it.

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00:13:19,000 --> 00:13:22,700
So it had minus 1 joules of work
done by the system, so

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these become pluses, and you
get back to a minus 4.

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Do whatever's intuitive
for you.

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For me, this tends to be the
most intuitive, where you

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don't even use a formula.

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We just think, if I'm doing
work, I'm using up energy.

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If I get work done to me, I'm
being handed over energy.

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If I have heat taken away from
me, I'm giving away energy.

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If I have heat added to me,
I'm getting energy.

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See you in the next video.